Piotr Antonik

Online Training of an Opto-Electronic Reservoir Computer Applied to Real-Time Channel Equalization

Reservoir computing is a bioinspired computing paradigm for processing time-dependent signals. The performance of its analog implementation is comparable to other state-of-the-art algorithms for tasks such as speech recognition or chaotic time series prediction, but these are often constrained by the offline training methods commonly employed. Here, we investigated the online learning approach by training an optoelectronic reservoir computer using a simple gradient descent algorithm, programmed on a field-programmable gate array chip. Our system was applied to wireless communications, a quickly growing domain with an increasing demand for fast analog devices to equalize the nonlinear distorted channels. We report error rates up to two orders of magnitude lower than previous implementations on this task. We show that our system is particularly well suited for realistic channel equalization by testing it on a drifting and a switching channel and obtaining good performances.

Towards pattern generation and chaotic series prediction with photonic reservoir computers

Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals that is particularly well suited for analog implementations. Our team has demonstrated several photonic reservoir computers with performance comparable to digital algorithms on a series of benchmark tasks such as channel equalisation and speech recognition. Recently, we showed that our opto-electronic reservoir computer could be trained online with a simple gradient descent algorithm programmed on an FPGA chip. This setup makes it in principle possible to feed the output signal back into the reservoir, and thus highly enrich the dynamics of the system. This will allow to tackle complex prediction tasks in hardware, such as pattern generation and chaotic and financial series prediction, which have so far only been studied in digital implementations. Here we report simulation results of our opto-electronic setup with an FPGA chip and output feedback applied to pattern generation and Mackey-Glass chaotic series prediction. The simulations take into account the major aspects of our experimental setup. We find that pattern generation can be easily implemented on the current setup with very good results. The Mackey-Glass series prediction task is more complex and requires a large reservoir and more elaborate training algorithm. With these adjustments promising result are obtained, and we now know what improvements are needed to match previously reported numerical results. These simulation results will serve as basis of comparison for experiments we will carry out in the coming months.

Brain-Inspired Photonic Signal Processor for Generating Periodic Patterns and Emulating Chaotic Systems

Reservoir computing is a bio-inspired computing paradigm for processing time-dependent signals. Its hardware implementations have received much attention because of their simplicity and remarkable performance on a series of benchmark tasks. In previous experiments the output was uncoupled from the system and in most cases simply computed offline on a post-processing computer. However, numerical investigations have shown that feeding the output back into the reservoir would open the possibility of long-horizon time series forecasting. Here we present a photonic reservoir computer with output feedback, and demonstrate its capacity to generate periodic time series and to emulate chaotic systems. We study in detail the effect of experimental noise on system performance. In the case of chaotic systems, this leads us to introduce several metrics, based on standard signal processing techniques, to evaluate the quality of the emulation. Our work significantly enlarges the range of tasks that can be solved by hardware reservoir computers, and therefore the range of applications they could potentially tackle. It also raises novel questions in nonlinear dynamics and chaos theory.

Online Training of an Opto-Electronic Reservoir Computer

Reservoir computing is a bioinspired computing paradigm for processing time-dependent signals. The performance of its analog implementation is comparable to other state-of-the-art algorithms for tasks such as speech recognition or chaotic time series prediction, but these are often constrained by the offline training methods commonly employed. Here, we investigated the online learning approach by training an optoelectronic reservoir computer using a simple gradient descent algorithm, programmed on a field-programmable gate array chip. Our system was applied to wireless communications, a quickly growing domain with an increasing demand for fast analog devices to equalize the nonlinear distorted channels. We report error rates up to two orders of magnitude lower than previous implementations on this task. We show that our system is particularly well suited for realistic channel equalization by testing it on a drifting and a switching channel and obtaining good performances.

Online Training for High-Performance Analogue Readout Layers in Photonic Reservoir Computers

Reservoir computing is a bio-inspired computing paradigm for processing time-dependent signals. The performance of its hardware implementation is comparable to state-of-the-art digital algorithms on a series of benchmark tasks. The major bottleneck of its implementations is the readout layer, based on slow offline post-processing. Few analogue solutions have been proposed, but all suffered from noticeable decrease in performance due to added complexity of the setup. Here, we propose the use of online training to solve these issues. We study the applicability of this method using numerical simulations of an experimentally feasible reservoir computer with an analogue readout layer. We also consider a nonlinear output layer, which would be very difficult to train with traditional methods. We show numerically that online learning allows to circumvent the added complexity of the analogue layer and obtain the same level of performance as with a digital layer. This work paves the way to high-performance fully analogue reservoir computers through the use of online training of the output layers.

Towards Adjustable Signal Generation with Photonic Reservoir Computers

Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals. We have recently reported the first opto-electronic reservoir computer trained online by an FPGA chip. This setup makes it in principle possible to feed the output signal back into the reservoir, which in turn allows to tackle complex prediction tasks in hardware. In present work, we investigate numerically the performance of an offline-trained opto-electronic reservoir computer with output feedback on four signal generation tasks. We report very good results and show the potential of such setup to be used as a high-speed analog control system.

Pattern and Frequency Generation Using an Opto-Electronic Reservoir Computer with Output Feedback

Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals. The performance of its analogue implementations matches other digital algorithms on a series of benchmark tasks. Their potential can be further increased by feeding the output signal back into the reservoir, which would allow to apply the algorithm to time series generation. This requires, in principle, implementing a sufficiently fast readout layer for real-time output computation. Here we achieve this with a digital output layer driven by an FPGA chip. We demonstrate the first opto-electronic reservoir computer with output feedback and test it on two examples of time series generation tasks: pattern and frequency generation. The good results we obtain open new possible applications for analogue Reservoir Computing.

Embodiment of Learning in Electro-Optical Signal Processors

Delay-coupled electro-optical systems have received much attention for their dynamical properties and their potential use in signal processing. In particular, it has recently been demonstrated, using the artificial intelligence algorithm known as reservoir computing, that photonic implementations of such systems solve complex tasks such as speech recognition. Here, we show how the backpropagation algorithm can be physically implemented on the same electro-optical delay-coupled architecture used for computation with only minor changes to the original design. We find that, compared to when the backpropagation algorithm is not used, the error rate of the resulting computing device, evaluated on three benchmark tasks, decreases considerably. This demonstrates that electro-optical analog computers can embody a large part of their own training process, allowing them to be applied to new, more difficult tasks.

Towards Online-Trained Analogue Readout Layer

This chapter presents the last project that I started with the OPERA-Photonique group. We proposes the use of online training in the context of analogue readout layers for photonic reservoir computers. We studied the applicability of this method using numerical simulations of an experimentally feasible reservoir computer with an analogue readout layer. We also considered a nonlinear output layer, which would be very difficult to train with traditional methods. We show numerically that online learning allows to circumvent the added complexity of the analogue layer and obtain the same level of performance as with a digital layer.

Online Training of a Photonic Reservoir Computer

This chapter presents an experiment that was not originally planned as part of my thesis. The project was set up when Michiel Hermans joined our team in 2015 with an idea of implementing the backpropagation training algorithm in hardware, using our opto-electronic reservoir computer with one slight modification. We found that, compared when the backpropagation algorithm is not used, the error rate of the resulting computing device, evaluated on three benchmark tasks, decreases considerably. This demonstrates that electro-optical analog computers can embody a large part of their own training process, allowing them to be applied to new, more difficult tasks.